3. The marginal product of labor curves corresponding to the production functions in problem 2 are as follows:

Workers Employed 10 20 30 40 50 60 70 80 90 100 MPL in Sector 1 1.51 1.14 0.97 0.87 0.79 0.74 0.69 0.66 0.63 0.60 MPL in Sector 2 1.59 1.05 0.82 0.69 0.61 0.54 0.50 0.46 0.43 0.40

a. Suppose that the price of good 2 relative to that of good 1 is 2. Determine graphically the wage rate and the allocation of labor between the two sectors.

b. Using the graph drawn for problem 2, determine the output of each sector. Then confirm graphically that the slope of the production possibility frontier at that point equals the relative price.

c. Suppose that the relative price of good 2 falls to 1. Repeat

(a) and (b).

d. Calculate the effects of the price change on the income of the specific factors in sectors 1 and 2.